While the Libyan army ducks Nato air strikes, a different kind of war is raging on Paris's Left Bank. French intellectuals who pushed Nicolas Sarkozy towards military intervention in Libya are now at each other's throats, calling into question the role of philosophers in influencing foreign policy.

Bernard-Henri Lévy, the celebrity philosopher who played a crucial role in Sarkozy's decision to recognise the rebel movement and intervene in Libya, is under attack by another leading intellectual, the writer and film-maker Claude Lanzmann.

Last month Lanzmann, a former partner of Simone de Beauvoir, signed Lévy's petition for urgent intervention in Libya. The support of the Paris intelligentsia helped Lévy to pile pressure on Sarkozy. After travelling to Libya in his trademark white shirt unbuttoned to the navel, the dandy philosopher known as BHL appealed directly to Sarkozy to intervene, and orchestrated an Élysée meeting with representatives of the Libyan opposition.

Despite being dismissed by one Élysée adviser as a "pretentious little bastard", BHL's influence over the president was unprecedented for a philosopher. He was soon being referred to as Sarkozy's "war chief" and "second foreign minister", and inspiring headlines such as "Plato 1, Nato 0". It was a sea change for French intellectuals: thinkers such as Jean-Paul Sartre may have influenced public opinion but they had never succeeded in directing French policy.

Now the intellectual support behind BHL is fragmenting. Last week Lanzmann withdrew his backing and opposed the action in Libya. He warned against "a war without name and an uncertain ending". In a front-page editorial, Le Monde said the intelligentsia spat might be "a very Parisian controversy" but revealed a real unease in Europe over the Libya endeavour. "Stalemate, disaccord and finally, failure: that is effectively what is threatening to happen," the paper wrote.

In a series of articles detailing a recent visit to Libya, Lévy shot back at Lanzmann's "crazy" turnaround. He maintained his support for the rebel movement and said he was convinced Gaddafi would leave Libya and "let the Libyan people alone decide their destiny".

In turn, Lanzmann stepped up his attacks, telling the magazine Marianne that he had signed BHL's appeal for intervention in haste after it popped up in his email inbox like a kind of "ultimatum". He said he had been shaken by the reality of the intervention and didn't care if he was now called a traitor.

Other Paris thinkers took sides. The pacifist philosopher Michel Onfray attacked BHL for personal "opportunism", comparing him to a long line of French philosophers from Sartre to André Malraux who were "better at writing their own myth than the history of the world".

The philosopher Regis Debray warned that French intellectuals became "comic" when they tried to interfere in foreign affairs. But the writer Renaud Camus defended BHL as part of the "best tradition of French intellectuals", and the philosopher Pascal Bruckner said Lévy was "profoundly respectable" in staying true to his convictions.

When Sarkozy launched the Libya offensive, he had the support of the vast spectrum of French politics, including the Socialists and the normally pacifist Greens, with the only criticism coming from the extreme-right Front National. The intervention is supported by a majority of the French public, but it hasn't directly boosted Sarkozy's record low poll ratings.